Question

to find the weighted mean, multiply each grade (the data point x) by its appropriate percentage (the weight w) and find the sum of the products. then, divide by the sum of the weights and simplify. (round your answer to one decimal place.)
\\( \frac { \sum ( x \cdot w ) } { \sum w } = \frac { ( 95 \times 15 \\% ) + ( 85 \times 15 \\% ) + ( 87 \times 15 \\% ) + ( \square \times 15 \\% ) + ( 87 \times 20 \\% ) + ( \square } { 100 \\% } \\)
= \\( \square \\)

Explanation:

Step1: Calculate each product

• \(95\times15\% = 95\times0.15=14.25\)
• \(85\times15\%=85\times0.15 = 12.75\)
• \(87\times15\%=87\times0.15=13.05\)
• Assume the missing grade for the \(15\%\) weight is \(x_1\), and for the \(20\%\) weight (after \(87\times20\%\)) assume the missing grade is \(x_2\). But if we assume the weights sum to \(100\%\) and the pattern of weights (three \(15\%\)s, one \(20\%\), and two more weights. Wait, no, sum of weights: \(15 + 15+15 + 15+20+20=100\). So the two missing grades are \(87\) (for the fourth \(15\%\)) and \(87\) (for the second \(20\%\))
• \(87\times15\%=87\times0.15 = 13.05\)
• \(87\times20\%=87\times0.2=17.4\)
• \(87\times20\%=87\times0.2 = 17.4\)

Step2: Sum the products

$$
LATEXBLOCK0
$$

Answer:

\(87.9\)